Golf ball

ABSTRACT

A golf ball can include a core, a mid layer, and a cover. The golf ball can satisfy the following mathematical formulas (1) and (2),(Fa/Fan)≤0.90  (1),(Fa/Fan)2/(Fp/Fpn)≤0.90  (2),wherein Fa represents a maximum vertical force of the golf ball measured under a first condition. Fan represents a maximum vertical force of a standard ball measured under the first condition, Fp represents a maximum vertical force of the golf ball measured under a second condition, and Fpn represents a maximum vertical force of the standard ball measured under the second condition.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of PatentApplication No. 2021-13-1161 filed in JAPAN on Aug. 19, 2021. The entiredisclosure and content of this application are hereby incorporated byreference.

BACKGROUND Field

The present specification discloses golf balls each having a core, a midlayer, and a cover.

Description of the Related Art

An interest to golf players concerning golf balls is flight performance.Golf players prefer a golf ball with which a large flight distance isachieved. Golf players also place importance on controllability of agolf ball. The controllability correlates with spin performance. Golfplayers further place importance on feel at impact of a golf ball.Generally, players prefer soft feel at impact.

A typical golf ball has a core, a mid layer, and a cover. JP2020-171623discloses improvements on a core, a mid layer, and a cover.

Golf players place importance on a flight distance upon a shot with amiddle iron as well as a flight distance upon a shot with a driver.

Golf players place importance on spin performance when a golf ball inthe rough is hit with a short iron.

Golf players place importance on reel at impact upon a shot with a shortiron. Players further place importance on feel at impact upon putting.

It is an intention of the applicant to provide a golf ball havingexcellent flight performance upon a shot with a middle iron, excellentspin performance upon a shot with a short iron, excellent feel at impactupon a shot with a short iron, and excellent feel at impact uponputting.

SUMMARY

A preferred golf ball includes a core, a mid layer positioned outsidethe core, and a cover positioned outside the mid layer, and satisfiesthe following mathematical formulas (1) and (2),

(Fa/Fan)≤0.90  (1),

(Fa/Fan)²/(Fp/Fpn)≤0.90  (2),

wherein Fa represents a maximum vertical force of the golf ball measuredunder a first condition, ran represents a maximum vertical force of astandard ball measured under the first, condition, Fp represents amaximum vertical force of the golf ball measured under a secondcondition, and Fpn represents a maximum vertical force of the standardball measured under the second condition.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a partially cutaway cross-sectional view schematically showinga golf ball according to an embodiment.

FIG. 2 is a front view showing a sand wedge for evaluating the golf ballin FIG. 1 .

FIG. 3 is a side view showing the sand wedge in FIG. 2 .

FIG. 4 is a plan view showing a putter for evaluating the golf ball inFIG. 1 .

FIG. 5 is a cross-sectional view taken along a line V-V in FIG. 4 .

DETAILED DESCRIPTION

The following will describe in detail preferred embodiments withappropriate reference to the drawings.

A golf ball 2 shown in FIG. 1 includes a spherical core 4, a mid layer 6positioned outside the core 4, a cover 8 positioned outside the midlayer 6, an inner paint layer 10 positioned outside the cover 8, and anouter paint layer 12 positioned outside the inner paint layer 10. Thenumber of paint layers is two. The outer paint layer 12 is a paint layerpositioned on the outermost, side. The number of paint layers may be oneor may be three or more. The golf ball 2 has a plurality of dimples 14on the surface thereof. Of the surface of the golf ball 2, a part otherthan the dimples 14 is a land 16. The golf ball 2 has a mark layer (notshown) on the external side of the cover 8.

The golf ball 2 preferably has a diameter of not less than 40 mm and notgreater than 45 mm. From the viewpoint of conformity to the rulesestablished by the United States Golf Association (USGA), the diameteris particularly preferably not less than 42.67 mm. From the viewpoint ofsuppression of air resistance, the diameter is more preferably notgreater than 44 mm and particularly preferably not greater than 42.80mm.

The golf ball 2 preferably has a weight of not less than 40 g and notgreater than 50 g. From the viewpoint of attainment of great inertia,the weight is more preferably not less than 44 g and particularlypreferably not less than 45.00 g. From the viewpoint of conformity tothe rules established by the USGA, the weight is particularly preferablynot greater than 45.93 g.

The core 4 is formed by crosslinking a rubber composition. Examples ofpreferable base rubbers for use in the rubber composition includepolybutadienes, polyisoprenes, styrene-butadiene copolymers,ethylene-propylene-diene copolymers, and natural rubbers. From theviewpoint of resilience performance of the core 4, polybutadienes arepreferable. When a polybutadiene and another rubber are used incombination, it is preferred if the polybutadiene is a principalcomponent. Specifically, the proportion of the polybutadiene to theentire base rubber is preferably not less than 50% by weight andparticularly preferably not less than 80% by weight. A polybutadiene inwhich the proportion of cis-1,4 bonds is not less than 80% isparticularly preferable.

The rubber composition of the core 4 preferably includes aco-crosslinking agent. Preferable co-crosslinking agents from theviewpoint of durability and resilience performance of the golf ball 2are monovalent or bivalent metal salts of an α,β-unsaturated carboxylicacid having 2 to 8 carbon atoms. Examples of preferable co-crosslinkingagents include zinc acrylate, magnesium acrylate, zinc methacrylate, andmagnesium methacrylate. From the viewpoint of resilience performance ofthe core 4, zinc acrylate and zinc methacrylate are particularlypreferable.

The rubber composition may include a metal oxide and an α,β-unsaturatedcarboxylic acid having 2 to 8 carbon atoms. They both react with eachother in the rubber composition to obtain a salt. The salt serves as aco-crosslinking agent. Examples of preferable α,β-unsaturated carboxylicacids include acrylic acid and methacrylic acid. Examples of preferablemetal oxides include zinc oxide and magnesium oxide.

The amount of the co-crosslinking agent per 100 parts by weight of thebase rubber is preferably not less than 10 parts by weight and notgreater than 45 parts by weight. The golf ball 2 in which this amount isnot less than 10 parts by weight has excellent resilience performance.From this viewpoint, this amount is more preferably not less than 15parts by weight and particularly preferably not less than 20 parts byweight. The golf ball 2 in which this amount is not greater than 45parts by weight has excellent feel at impact. From this viewpoint, thisamount is more preferably not greater than 40 parts by weight andparticularly preferably not greater than 35 parts by weight.

Preferably, the rubber composition of the core 4 includes an organicperoxide. The organic peroxide serves as a crosslinking initiator. Theorganic peroxide contributes to the resilience performance of the core4. Examples of suitable organic peroxides include dicumyl peroxide,1,1-bis(t-butylperoxy)-3,3,5-trimethylcyclohexane,2,5-dimethyl-2,5-di(t-butylperoxy) hexane, and di-t-butyl peroxide. Anorganic peroxide with particularly high versatility is dicumyl peroxide.

The amount of the organic peroxide per 100 parts by weight of the baserubber is preferably not less than 0.1 parts by weight and not greaterthan 3.0 parts by weight. The golf ball 2 in which this amount is notless than 0.1 parts by weight has excellent resilience performance. Fromthis viewpoint, this amount is more preferably not less than 0.3 partsby weight and particularly preferably not less than 0.5 parts by weight.The golf ball 2 in which this amount is not greater than 3.0 parts byweight has excellent feel at impact. From this viewpoint, this amount ismore preferably not greater than 2.5 parts by weight and particularlypreferably not greater than 2.0 parts by weight.

Preferably, the rubber composition of the core 4 includes an organicsulfur compound. The organic sulfur compound contributes to theresilience performance of the core 4. Organic sulfur compounds includenaphthalenethiol compounds, benzenethiol compounds, and disulfidecompounds.

Examples of naphthalenethiol compounds include 1-naphthalenethiol,2-napnthalenethiol, 4-chloro-1-naphthalenethiol,4-bromo-1-naphthalenethiol, 1-chloro-2-naphthalenethiol,1-bromo-2-naphthalenethiol, 1-fluoro-2-naphthalenethiol,1-cyano-2-naphthalenethiol, and 1-acetyl-2-naphthalenethiol.

Examples of benzenethiol compounds include benzenthiol,4-chlorobenzenethiol, 3-chlorobenzenethiol, 4-bromobenzenethiol,3-bromobenzenethiol, 4-fluorobenzenethiol, 4-iodobenzenethiol,2,5-dichlorobenzenethiol, 3,5-dichlorobenzenethiol,2,6-dichlorobenzenethiol, 2,5-dibromobenzenthiol,3,5-dibromobenzenethiol, 2-chloro-5-bromobenzenethiol,2,4,6-trichlorobenzenethiol, 2,3,4,5,6-pentachlorobenzenethiol,2,3,4,5,6-pentafluorobenzenethiol, 4-cyanobenzenethiol,2-cyanobenzenethiol, 4-nitrobenzenethiol, and 2-nitrobenzenethiol.

Examples of disulfide compounds include diphenyl disulfide,bis(4-chlorophenyl)disulfide, bis(3-chlorophenyl)disulfide,bis(4-bromophenyl)disulfide, bis(3-bromophenyl)disulfide,bis(4-fluorophenyl)disulfide, bis(4-iodophenyl)disulfide,bis(4-cyanophenyl)disulfide, bis(2,5-dichlorophenyl) disulfide,bis(3,5-dichlorophenyl) disulfide, bis(2,6-dichlorophenyl)disulfide,bis(2,5-dibromphenyl)disulfide, bis(3,5-dibromphenyl)disulfide,bis(2-chloro-5-bromophenyl) disulfide,bis(2-cyano-5-bromophenyl)disulfide,bis(2,4,6-trichlorophenyl)disulfide, bis(2-cyano-4-chloro-6-bromophenyl)disulfide, bis(2,3,5,6-tetrachlorophenyl)disulfide,bis(2,3,4,5,6-pentachlorophenyl)disulfide, andbis(2,3,4,5,6-pentabromophenyl)disulfide.

From the viewpoint of resilience performance, the amount of the organicsulfur compound per 100 parts by weight of the base rubber is preferablynot less than 0.1 parts by weight, more preferably not less than 0.2parts by weight, and particularly preferably not less than 0.3 parts byweight. From the viewpoint of soft feel at impact, this amount ispreferably not greater than 1.5 parts by weight, more preferably notgreater than 1.0 part by weight, and particularly preferably not greaterthan 0.3 parts by weight. Two or more organic sulfur compounds may beused in combination.

The rubber composition of the core 4 may include a carboxylic acid or acarboxylate. The carboxylic acid and the carboxylate can contribute tomaking the hardness distribution of the core 4 appropriate. An exampleof preferable carboxylic acids is benzoic acid. Examples of preferablecarboxylates include zinc octoate and zinc stearate.

The rubber composition of the core 4 may include a filler for thepurpose of specific gravity adjustment and the like. Examples ofsuitable fillers include zinc oxide, barium sulfate, calcium carbonate,and magnesium carbonate. The amount of the filler is determined asappropriate so that the intended specific gravity of the core 4 isachieved.

The rubber composition of the core 4 may include various additives, suchas sulfur, an anti-aging agent, a coloring agent, a plasticizer, adispersant, and the like, in an adequate amount. The rubber compositionmay include crosslinked rubber powder or synthetic resin powder.

The core 4 preferably has a diameter D1 of not less than 35.0 mm and notgreater than 40.7 mm. The golf ball 2 that includes the core 4 having adiameter D1 of not less than 35.0 mm has excellent resilienceperformance. From this viewpoint, the diameter D1 is more preferably notless than 37.0 mm and particularly preferably not less than 38.0 mm. Thegolf ball 2 that includes the core 4 having a diameter D1 of not greaterthan 40.7 mm has excellent durability. From this viewpoint, the diameterD1 is more preferably not greater than 40.3 mm and particularlypreferably not greater than 40.0 mm.

The core 4 preferably has a central hardness H1o of not less than 45 andnot greater than 70. The golf ball 2 that includes the core 4 having acentral hardness H1o of not less than 45 has excellent resilienceperformance. From this viewpoint, the central hardness H1o is morepreferably not less than 43 and particularly preferably not less than50. The golf ball 2 that includes the core 4 having a central hardnessH1o of not greater than 70 has excellent feel at impact. From thisviewpoint, the central hardness H1o is more preferably not greater than67 and particularly preferably not greater than 65.

The central hardness H1o is measured with a Shore C type hardness scalemounted to an automated hardness meter (trade name “digi test II”manufactured by Heinrich Bareiss Prüfgerätebau GmbH). The hardness scaleis pressed against, the central point of the cross-section of ahemisphere obtained by cutting the golf ball 2. The measurement isconducted in an environment of 23° C.

A hardness H1₍₁₀₎ of the core 4 at a point at which a distance from thecentral point of the core 4 is 10 mm is preferably not less than 55 andnot greater than 85. The golf ball 2 that includes the core 4 having ahardness H1₍₁₀₎ of not less than 55 has excellent resilienceperformance. From this viewpoint, the hardness is more preferably notless than 58 and particularly preferably not leas than 60. The golf ball2 that includes the core 4 having a hardness H1₍₁₀₎ of not greater than85 has excellent feel at impact. From this viewpoint, the hardnessH1₍₁₀₎ is more preferably not greater than 82 and particularlypreferably not greater than 80.

The hardness H1₍₁₀₎ is measured with a Shore C type hardness scalemounted to an automated hardness meter (trade name “digi test II”manufactured by Heinrich Bareiss Prüfgerätebau GmbH). The hardness scaleis pressed against a position away from the central point by 10 mm onthe cross-section of a hemisphere obtained by cutting the golf ball 2.The measurement is conducted in an environment of 23° C.

The core 4 preferably has a surface hardness H1s of not less than 70 andnot greater than 90. The golf ball 2 that includes the core 4 having asurface hardness H1s of not less than 70 has excellent resilienceperformance. From this viewpoint, the surface hardness H1s is morepreferably not less than 73 and particularly preferably not less than75. The golf ball 2 that includes the core 4 having a surface hardnessH1s of not greater than 90 has excellent feel at impact. From thisviewpoint, the surface hardness H1s is more preferably not greater than87 and particularly preferably not greater than 85.

The surface hardness H1s is measured with a Shore C type hardness scalemounted to an automated hardness meter (trade name “digi test II”manufactured by Heinrich Bareiss Prüfgerätebau GmbH). The hardness scaleis pressed against the surface of the core 4. The measurement isconducted in an environment of 23° C.

The difference (H1s−H1o) between the surface hardness H1s and thecentral hardness H1o is preferably not less than 14. The golf ball 2that includes the core 4 having a difference (H1s−H1o) of not less than14 has excellent flight performance upon a shot with a middle iron. Thegolf ball 2 further has excellent feel at impact upon a shot with ashort iron and upon putting. From these viewpoints, the difference(H1s−H1o) is more preferably not less than 16 and particularlypreferably not less than 18. From the viewpoint of durability of thegolf ball 2, the difference (H1s−H1o) is preferably not greater than 30.

The difference (H1s−H1₍₁₀₎) between the surface hardness H1s and thehardness H1₍₁₀₎ at the point at which the distance from the centralpoint of the core 4 is 10 mm is preferably not less than 7. The golfball 2 that includes the core 4 having a difference (H1s−H1₍₁₀₎) of notless than 7 has low spin upon a shot with a driver and therefore hasexcellent flight performance. The golf ball 2 further has excellent feelat impact upon an approach shot and upon putting. From these viewpoints,the difference (H1s−H1₍₁₀₎) more preferably not less than 8 andparticularly preferably not less than 9. From the viewpoint ofdurability of the golf ball 2, the difference (H1s−H1₍₁₀₎) is preferablynot greater than 15.

The core 4 preferably has a weight of not less than 10 g and not greaterthan 42 g. The temperature for crosslinking the core 4 is typically notlower than 140° C. and not higher than 180° C. The time period forcrosslinking the core 4 is typically not shorter than 10 minutes and notlonger than 60 minutes.

The mid layer 6 is positioned outside the core 4. The mid layer 6 isformed from a thermoplastic resin composition. Examples of the basepolymer of the resin composition include ionomer resins, thermoplasticpolyester elastomers, thermoplastic polyamide elastomers, thermoplasticpolyurethane elastomers, thermoplastic polyolefin elastomers, andthermoplastic polystyrene elastomers. Ionomer resins are particularlypreferable. Ionomer resins are highly elastic. The golf ball 2 thatincludes the mid layer 6 including an ionomer resin has excellentresilience performance. The golf ball 2 has excellent flightperformance.

An ionomer resin and another resin may be used in combination. In thiscase, from the viewpoint of resilience performance, the ionomer resin isincluded as the principal component of the base polymer. The proportionof the ionomer resin to the entire base polymer is preferably not lessthan 50% by weight.

Examples of preferable ionomer resins include binary copolymers formedwith an α-olefin and an α,β-unsaturated carboxylic acid having 3 to 8carbon atoms. A preferable binary copolymer includes 80% by weight ormore but 30% by weight or less of an α-olefin, and 10% by weight or merebut 20% by weight or less of an α,β-unsaturated carboxylic acid. Thebinary copolymer has excellent resilience performance. Examples of otherpreferable ionomer resins include ternary copolymers formed with: anα-olefin; an α,β-unsaturated carboxylic acid having 3 to 8 carbon atoms;and an α,β-unsaturated carboxylate ester having 2 to 22 carbon atoms. Apreferable ternary copolymer includes 70% by weight or more but 85% byweight or less of an α-olefin, 5% by weight or more but 30% by weight orless of an α,β-unsaturated carboxylic acid, and 1% by weight or more but25% by weight or less of an α,β-unsaturated carboxylate ester. Theternary copolymer has excellent resilience performance. For the binarycopolymer and the ternary copolymer, preferable α-olefins are ethyleneand propylene, while preferable α,β-unsaturated carboxylic acids areacrylic acid and methacrylic acid. A particularly preferable ionomerresin is a copolymer formed with ethylene and acrylic acid. Anotherparticularly preferable ionomer resin is a copolymer formed withethylene and methacrylic acid.

In the binary copolymer and the ternary copolymer, some of the carboxylgroups are neutralized with metal ions. Examples of metal ions for usein neutralization include sodium ions, potassium ions, lithium ions,zinc ions, calcium ions, magnesium ions, aluminum ions, and neodymiumions. The neutralization may be carried out with two or more types ofmetal ions. Particularly suitable metal ions from the viewpoint ofresilience performance and durability of the golf ball 2 are sodiumions, zinc ions, lithium ions, and magnesium ions.

Specific examples of ionomer resins include trade names “Himilan 1555”,“Himilan 1557”, “Himilan 1605”, “Himilan 1706”, “Himilan 1707”, “Himilan1856”, “Himilan 1855”, “Himilan AM7311”, “Himilan AM7315”, “HimilanAM7317”, “Himilan AM7329”, and “Himilan AM7337”, manufactured by DuPont-MITSUI POLYCHEMICALS Co., Ltd.; trade names “Surlyn 6120”, “Surlyn6910”, “Surlyn 7930”, “Surlyn 7940”, “Surlyn 8140”, “Surlyn 8150”,“Surlyn 8940”, “Surlyn 8945”, “Surlyn 9120”, “Surlyn 9150”, “Surlyn9910”, “Surlyn 9545”, “Surlyn AD8546”, “HPF1000”, and “HPF2000”,manufactured by E.I. du Pent de Nemours and Company; and trade names“IOTEK 7010”, “IOTEK 7030”, “IOTEK 7510”, “IOTEK 7520”, “IOTEK 8000”,and “IOTEK 8030”, manufactured by ExxonMobil Chemical Corporation. Twoor more ionomer resins may be used in combination.

The resin composition of the mid layer 6 may include a coloring agent, afiller, a dispersant, an antioxidant, an ultraviolet absorber, a lightstabilizer, a fluorescent material, a fluorescent brightener, and thelike in an adequate amount. When the hue of the golf ball 2 is white, atypical coloring agent is titanium dioxide.

The mid layer 6 preferably has a thickness T2 of not less than 0.5 mmand not greater than 2.0 mm. The golf ball 2 in which the thickness T2is not less than 0.5 mm has excellent resilience performance. From thisviewpoint, the thickness T2 is more preferably not less than 0.7 mm andparticularly preferably not less than 0.9 mm. The golf ball 2 in whichthe thickness T2 is not greater than 2.0 mm has excellent feel atimpact. From this viewpoint, the thickness T2 is preferably not greaterthan 1.7 mm and particularly preferably not greater than 1.5 mm. Thethickness T2 is measured at a position immediately below the land 16.

The mid layer 6 preferably has a material hardness H2 of not less than55 and not greater than 75. The golf ball 2 in which the hardness H2 isnot less than 55 has excellent resilience performance. From thisviewpoint, the hardness H2 is more preferably not less than 58 andparticularly preferably not less than 60. The golf ball 2 in which thehardness H2 is not greater than 75 has excellent feel at impact. Fromthis viewpoint, the hardness H2 is more preferably not greater than 72and particularly preferably not greater than 70.

The hardness H2 of the mid layer 6 is measured according to thestandards of “ASTM-D 2240-68”. The hardness H2 is measured with a ShoreD type hardness scale mounted to an automated hardness meter (trade name“digi test II” manufactured by Heinrich Bareiss Prüfgerätebau GmbH). Forthe measurement, a sheet that is formed by hot press, is formed from thesame material as that of the mid layer 6, and has a thickness of about 2mm, is used. Prior to the measurement, a sheet is kept at 23° C. for twoweeks. At the time of measurement, three sheets are stacked.

The mid layer 6 preferably has a surface hardness H2s of not less than85 and not greater than 100. The golf ball 2 in which the surfacehardness H2s is not less than 85 has excellent resilience performance.From this viewpoint, the surface hardness H2s is more preferably notless than 88 and particularly preferably not less than 90. The golf ball2 in which the surface hardness H2s is not greater than 100 hasexcellent feel at impact. From this viewpoint, the surface hardness H2sis more preferably not greater than 98 and particularly preferably notgreater than 96.

The surface hardness H2s is measured with a Shore C type hardness scalemounted to an automated hardness meter (trade name “digi test II”manufactured by Heinrich Bareiss Prüfgerätebau GmbH). The hardness scaleis pressed against the surface of a sphere consisting of the core 4 andthe mid layer 6. The measurement is conducted in an environment of 23°C.

The cover 8 is formed from a resin composition. Examples of the basepolymer of the resin composition include polyurethanes, ionomer resins,polyesters, polyamides, polyolefins, and polystyrenes. A preferable basepolymer from the viewpoint of feel, at impact and spin performance is apolyurethane. When a polyurethane and another resin are used incombination for the cover 8, the proportion of the polyurethane to theentire base resin is preferably not less than 50% by weight, morepreferably not less than 60% by weight, and particularly preferably notless than 70% by weight.

The resin composition of the cover 8 may include a thermoplasticpolyurethane or may include a thermosetting polyurethane. From theviewpoint of productivity of the golf ball 2, the thermoplasticpolyurethane is preferable. The thermoplastic polyurethane includes apolyurethane component, as a hard segment, and a polyester component ora polyether component as a soft segment. The thermoplastic polyurethaneis flexible. The cover 8 in which the polyurethane is used has excellentscuff resistance.

The thermoplastic polyurethane has a urethane bond within the molecule.The urethane bond can be formed by reacting a polyol with apolyisocyanate. The polyol, as a material for the urethane bond, has aplurality of hydroxyl groups. Low-molecular-weight polyols andhigh-molecular-weight polyols can be used.

Examples of low-molecular-weight polyols include diols, triols,tetraols, and hexaols. Specific examples of diols include ethyleneglycol, diethylene glycol, triethylene glycol, 1,2-propanediol,1,3-propanediol, 2-methyl-1,3-propanediol, dipropylene glycol,1,2-butanediol, 1,3-butanediol, 1,4-butanediol, 2,3-butanediol,2,3-dimethyl-2,3-butanediol, neopentyl, glycol, pentanediol, hexanediol,heptanediol, octanediol, and 1,6-cyclohexanedimethylol. Aniline diols orbisphenol A diols may be used. Specific examples of triols includeglycerin, trimethylol propane, and hexanetriol. Specific examples oftetraols include pentaerythritol and sorbitol.

Examples of high-molecular-weight polyols include: polyether polyolssuch as polyoxyethylene glycol (PEG), polyoxypropylene glycol (PPG), andpolytetraraethylene ether glycol (PTMG); condensed polyester polyolssuch as polyethylene adipate (PEA), polybutylene adipate (PBA), andpolyhexamethylene adipate (PHMA); lactone polyester polyols such aspoly-ε-caprolactone (PCL); polycarbonate polyols such aspolyhexamethylene carbonate; and acrylic polyols. Two or more polyolsmay be used in combination. From the viewpoint of feel at impact of thegolf ball 2, the high-molecular-weight polyol has a number averagemolecular weight of preferably not less than 400 and more preferably notless than 1000. The number average molecular weight is preferably notgreater than 10000.

Examples of polyisocyanates, as a material for the urethane bond,include aromatic diisocyanates, alicyclic diisocyanates, and aliphaticdiisocyanates. Two or more types of diisocyanates may be used incombination.

Examples of aromatic diisocyanates include 2,4-toluene diisocyanate,2,6-toluene diisocyanate, 4,4′-diphenylmethane diisocyanate (MDI),1,5-naphthylene diisocyanate (NDI), 3,3′-bitolylene-4,4′-diisocyanate(TODI), xylylene diisocyanate (XDI), tetramethylxylylene diisocyanate(TMXDI), and paraphenylene diisocyanate (PPDI). One example of aliphaticdiisocyanates is hexamethylene diisocyanate (HDI). Examples of alicyclicdiisocyanates include 4,4′-dicyclohexylmethane diisocyanate (H12MDI),1,3-bis(isocyanatemethyl)cyclohexane (H₈XDI), isophorone diisocyanate(IPDI), and trans-1,4-cyclohexane diisocyanate (CHDI).4,4′-dicyclohexylmethane diisocyanate is preferable.

Specific examples of the thermoplastic polyurethane include trade names“Elastollan NY80A”, “Elastollan NY82A”, “Elastollan NY83A”, “ElastollanNY84A”, “Elastollan NY85A”, “Elastollan NY88A”, “Elastollan NY90A”,“Elastollan NY95A”, “Elastollan NY97A”, “Elastollan NY585”, and“Elastollan KP016N”, manufactured by BASF Japan Ltd.; and trade names“RESAMINE P4585LS” and “RESAMINE PS62490”, manufactured by DainichiseikaColor & Chemicals Mfg. Co., Ltd.

The resin composition of the cover 8 may include a coloring agent, afiller, a dispersant, an antioxidant, an ultraviolet absorber, a lightstabilizer, a fluorescent material, a fluorescent brightener, alubricant, and the like in an adequate amount. When the hue of the golfball 2 is white, a typical coloring agent is titanium dioxide.

The cover 8 preferably has a thickness T3 of not less than 0.3 mm andnot greater than 1.5 mm. The golf ball 2 in which the thickness T3 isnot less than 0.3 mm has excellent controllability and feel at impact.From this viewpoint, the thickness T3 is more preferably not less than0.4 mm and particularly preferably not less than 0.5 mm. The golf ball 2in which the thickness T3 is not greater than 1.5 mm has excellentresilience performance. From this viewpoint, the thickness T3 is morepreferably not greater than 1.0 mm and particularly preferably notgreater than 0.8 mm. The thickness T3 is measured at a positionimmediately below the land 16.

The cover 8 preferably has a material hardness H3 of not less than 20and not greater than 45. The golf ball 2 in which the hardness H3 is notless than 20 has excellent durability. From this viewpoint, the hardnessH3 is more preferably not less than 25 and particularly preferably notless than 28. The golf ball 2 in which the hardness H3 is not greaterthan 45 has excellent controllability and feel at impact. From thisviewpoint, the hardness H3 is more preferably not greater than 40 andparticularly preferably not greater than 35.

The hardness H3 of the cover 8 is measured according to the standards of“ASTM-D 2240-68”. The hardness H3 is measured with a Shore D typehardness scale mounted to an automated hardness meter (trade name “digitest II” manufactured by Heinrich Bareiss Prüfgerätebau GmbH). For themeasurement, a sheet that is formed by hot press, is formed from thesame material as that of the cover 8, and has a thickness of about 2 mm,is used. Prior to the measurement, a sheet is kept at 23° C. for twoweeks. At the time of measurement, three sheets are stacked.

The cover 8 preferably has a surface hardness H3s of not less than 70and not greater than 95. The golf ball 2 in which the surface hardnessH3s is not less than 70 has excellent resilience performance. From thisviewpoint, the surface hardness H3s is more preferably not less than 75and particularly preferably not less than 80. The golf ball 2 in whichthe surface hardness H3s is not greater than 95 has excellent feel atimpact. From this viewpoint, the surface hardness H3s is more preferablynot greater than 92 and particularly preferably not greater than 90.

The surface hardness H3s is measured with a Shore C type hardness scalemounted to an automated hardness meter (trade name “digi test II”manufactured by Heinrich Bareiss Prüfgerätebau GmbH). The hardness scaleis pressed against the surface of a sphere consisting of the core 4, themid layer 6, and the cover 8. The measurement is conducted in anenvironment of 23° C.

The golf ball 2 may include a reinforcing layer between the mid layer 6and the cover 8. The reinforcing layer firmly adheres to the mid layer 6and also to the cover 8. The reinforcing layer suppresses separation ofthe cover 8 from the mid layer 6. The reinforcing layer is formed from aresin composition. Examples of a preferable base polymer of thereinforcing layer include two-component curing type epoxy resins andtwo-component curing type urethane resins. The reinforcing layerpreferably has a thickness of not less than 5 μm and not greater than 30μm.

The ratio ((T2+T3)/D1) of the sum (T2+T3) of the thickness T2 of the midlayer 6 and the thickness T3 of the cover 8 to the diameter D1 of thecore 4 is preferably not greater than 0.042. The golf ball 2 in whichthis ratio is not greater than 0.042 has excellent flight performanceupon a shot with a middle iron. From this viewpoint, the ratio((T2+T3)/D1) is more preferably not greater than 0.040 and particularlypreferably not greater than 0.038. From the viewpoint of durability ofthe golf ball 2, the ratio ((T2+T3)/D1) is preferably not less than0.032.

The ratio (H2/H3) of the hardness H2 of the mid layer 6 to the hardnessH3 of the cover 8 is preferably not less than 1.80. The golf ball 2 inwhich the ratio (H2/H3) is not less than 1.80 has excellent, flightperformance upon a shot with a middle iron. The golf ball 2 further hasexcellent feel at impact upon a shot with a middle iron and uponputting. From these viewpoints, the ratio (H2/H3) is more preferably notless than 2.00 and particularly preferably not less than 2.10. The ratio(H2/H3) is preferably not greater than 3.00.

Preferably, the surface hardness H2s of the mid layer 6 is greater thanthe surface hardness H1s of the core 4 and is greater than the surfacehardness H3s of the cover 8. The golf ball 2 has excellent flightperformance upon a shot with a middle iron. The golf ball 2 hasexcellent spin performance upon a shot with a middle iron. The golf ball2 further has excellent feel at impact upon a shot with a middle ironand upon putting. From these viewpoints, the difference (H2s−H1s) ispreferably not less than 6, more preferably not less than 8, andparticularly preferably not less than 11. The difference (H2s−H1s) ispreferably not greater than 20. The difference (H2s−H3s) is preferablynot less than 3, more preferably not less than 5, and particularlypreferably not less than 7. The difference (H2s−H3s) is preferably notgreater than 15.

The inner paint layer 10 is formed from a resin composition. Examples ofthe base resin of the resin composition include urethane resins, epoxyresins, acrylic resins, vinyl acetate resins, and polyester resins.Particularly preferable base resins are urethane resins. The inner paintlayer 10 preferably has a thickness of not less than 5 m and not greaterthan 20 μm.

The outer paint layer 12 is formed from a resin composition. Examples ofthe base resin of the resin composition include urethane resins, epoxyresins, acrylic resins, vinyl acetate resins, and polyester resins.Particularly preferable base resins are urethane resins. The cuter paintlayer 12 preferably has a thickness of not less than 5 μm and notgreater than 20 μm.

Typically, the inner paint layer 10 is formed from a polyurethane paint,and the outer paint layer 12 is formed from another polyurethane paint.A preferable polyurethane paint, includes a base material and a curingagent. The base material is a polyol composition (A), and the curingagent is a polyisocyanate composition (B).

The polyol composition (A) contains a polyol compound. The polyolcompound has two or more hydroxyl groups within the molecule thereof.The polyol compound may be a polyol compound (a1) having a hydroxylgroup at an end of the molecular chain thereof, or may be a polyolcompound (a2) having a hydroxyl group at a portion of the molecularchain other than the ends thereof. The polyol composition (A) maycontain two or more polyol compounds.

Examples of the polyol compound (a1) having a hydroxyl group at an endof the molecular chain thereof include: diols such as ethylene glycol,diethylene glycol, triethylene glycol, 1,3-butanediol, 1,4-butanediol,neopentyl glycol, and 1,6-hexanediol; and triols such as glycerin,trimethylol propane, and hexanetriol. Other examples of the polyolcompound (a1) having a hydroxyl group at an end of the molecular chainthereof include: polyether polyols, polyester polyols, polycaprolactonepolyols, polycarbonate polyols, urethane polyols, and acrylic polyols.Examples of polyether polyols include polyoxyethylene glycol (PEG),polyoxypropylene glycol (PPG), and polyoxytetramethylene glycol (PTMG).Examples of polyester polyols include polyethylene adipate diol,polybutylene adipate diol, and polyhexamethylene adipate diol. Examplesof polycaprolactone polyols include poly-ε-caprolactone diol. Examplesof polycarbonate polyols include polyhexamethylene carbonate diol.

Examples of the polyol compound (a2) having a hydroxyl group at theportion of the molecule other than the ends thereof include a modifiedpolyrotaxane having a hydroxyl group, and a hydroxyl group-modifiedvinyl chloride-vinyl acetate copolymer.

The polyisocyanate composition (B) contains a polyisocyanate compound.The polyisocyanate compound has two or more isocyanate groups. Examplesof the polyisocyanate compound include: aromatic diisocyanates such as2,4-toluene diisocyanate, 2,6-toluene diisocyanate, a mixture (TDI) of2,4-toluene diisocyanate and 2,6-toluene diisocyanate,4,4′-diphenylmethane diisocyanate (MDI), 1,5-naphthylene diisocyanate(NDI), 3,3′ -bitolylene-4,4′-diisocyanate (TODI), xylylene diisocyanate(XDI), tetramethylxylylene diisocyanate (TMXDI), and paraphenylenediisocyanate (PPDI); alicyclic or aliphatic diisocyanates such as4,4′-dicyclohexylmethane diisocyanate (H₁₂MDI), hydrogenated xylylenediisocyanate (H₆XDI), hexamethylene diisocyanate (HDI), isophoronediisocyanate (IPDI), and norbornene diisocyanate (NBDI); andtriisocyanates such as an allophanate product, a biuret product, anisocyanurate product, and an adduct product of diisocyanates. Thepolyisocyanate composition (B) may include two or more polyisocyanatecompounds.

The outer paint layer 12 preferably has an indentation depth of not lessthan 300 nm. The golf ball 2 that includes the outer paint layer 12having an indentation depth of not less than 300 nm has excellent spinperformance upon a shot with a short iron. The golf ball 2 further hasexcellent feel at impact upon a shot with a short iron and upon putting.From this viewpoint, the indentation depth is more preferably not lessthan 500 nm and particularly preferably not less than 700 nm. From theviewpoint of durability of the outer paint layer 12, the indentationdepth is preferably not greater than 3000 nm.

In measurement of the indentation depth, the golf ball 2 is divided toobtain a hemisphere. On the hemisphere, a cross-section passing throughthe central point of the golf ball 2 is exposed. The cross-sectionincludes a cross-section of the outer paint layer 12. The cross-sectionof the hemisphere is made horizontal by a cryo-microtome. A penetratorof a nanoindenter is brought into contact with the cross-section of theouter paint layer 12 and pressed against the cross-section in adirection perpendicular to the cross-section. Due to this pressing, thepenetrator advances. The pressing is continued until the load of thepenetrator reaches 50 mgf. The advancing distance of the penetrator whenthe load of the penetrator is 30 mgf is measured as an indentationdepth. The measurement conditions are as follows.

-   -   Nanoindenter: “ENT-2100” manufactured by ELIONIX INC.    -   Temperature: 30° C.    -   Penetrator: Berkovich penetrator (65.03° As(h)=26.43 h2)    -   Number of partitions: 500 steps    -   Step interval: 20 msec (100 mgf)

The golf ball 2 preferably has an amount of compressive deformation CDof not less than 3.00 mm. The golf ball 2 having an amount ofcompressive deformation CD of not less than 3.00 mm has excellent spinperformance upon a shot with a short iron. The golf ball 2 further hasexcellent feel at impact upon a shot with a short iron and upon putting.From this viewpoint, the amount of compressive deformation CD is morepreferably not less than 3.15 mm and particularly preferably not lessthan 3.25 mm. From the viewpoint of flight performance upon a shot witha middle iron, the amount of compressive deformation CD is preferablynot greater than 4.00 mm.

The amount of compressive deformation CD is measured with a YAMADA typecompression tester “SCH”. In the measurement, the golf ball 2 is placedon a hard plate made of metal. Next, a cylinder made of metal graduallydescends toward the golf ball 2. The golf ball 2, squeezed between thebottom face of the cylinder and the hard plate, becomes deformed. Amigration distance of the cylinder, starting from the state in which aninitial load of 98 N is applied to the golf ball 2 up to the state inwhich a final load of 1275 N is applied thereto, is measured. A movingspeed of the cylinder until the initial load is applied is 0.83 mm/s. Amoving speed of the cylinder after the initial load is applied until thefinal load is applied is 1.67 mm/s.

In the present specification, a maximum vertical force of the golf ball2 is measured under a first condition and a second condition. In thepresent specification, a maximum vertical force of a standard ball isalso measured under the first condition and the second condition.

The specifications of the standard ball are as follows:

Core

-   -   Diameter: 39.0 mm    -   Central hardness: 62 (Shore C)    -   Hardness at point at which distance from central point is 10 mm:        71 (Shore C)    -   Surface hardness: 78 (Shore C)

Mid layer

-   -   Thickness: 1.4 mm    -   Material hardness: 71 (Shore D)    -   Surface hardness: 97 (Shore C)

Cover

-   -   Thickness: 0.5 mm    -   Material hardness: 40 (Shore D)    -   Surface hardness: 87 (Shore C)

Paint layer

-   -   Thickness: 10 μm    -   Indentation depth: 971 nm    -   Amount of compressive deformation CDn: 3.12 mm

In production of the standard ball, a rubber composition is obtained bykneading 100 parts by weight of a high-cis polybutadiene (trade name“BR-60”, manufactured by JSR Corporation), 24.3 parts by weight of zincacrylate, 5.0 parts by weight of zinc oxide, 12.4 parts by weight ofbarium sulfate, and 0.6 parts by weight of dicumyl peroxide (DCP). Thisrubber composition is placed into a mold including upper and lower moldhalves each having a hemispherical cavity, and heated to obtain a corewith a diameter of 39.0 mm. A resin composition is obtained by kneading50 parts by weight of an ionomer resin (the aforementioned “Surlyn8150”), 50 parts by weight of another ionomer resin (the aforementioned“Surlyn 9150”), 4 parts by weight of titanium dioxide, and 9 parts byweight of barium sulfate with a twin-screw kneading extruder. The coreis placed into a mold including upper and lower mold halves each havinga hemispherical cavity. The core is covered with the resin compositionby injection molding to form a mid layer. The thickness of the mid layeris 1.4 mm. A resin composition is obtained by kneading theaforementioned PTMG and TDI at a ratio that can achieve a Shore Dhardness of 40. A final mold including upper and lower mold halves eachhaving a hemispherical cavity and having a large number of pimples onits cavity face is heated to a temperature of not lower than 80° C. andnot higher than 100° C. The resin composition is placed into the finalmold, the sphere including the core and the mid layer is further placedthereinto, and a cover is formed by compression molding. The thicknessof the cover is 0.5 mm. Dimples having a shape that is the invertedshape of the pimples are formed on the cover. A clear paint including atwo-component curing type polyurethane as a base material is applied tothe cover. The paint is dried to obtain a standard golf ball.

In the first condition, the golf ball 2 or the standard ball is hit witha sand wedge 18 (trade name “RTX-3”, manufactured by Roger ClevelandGolf Company, Inc.) shown in FIGS. 2 and 3 . FIGS. 2 and 3 also show afixing tool 19 and an acceleration sensor 20 (trade name “356A01”,manufactured by TOYO Corporation). The sand wedge 18 has a head 22, ashaft 24, and a grip 26. The loft angle of the head 22 is 58°. The brandname of the shaft 24 is “DG-S200” of TRUE TEMPER SPORTS, INC. The flexof the shaft 24 is S200. The acceleration sensor 20 is fixed to theshaft 24 via the fixing tool 19. The acceleration sensor 20 and the grip26 are separated from each other by 10 mm. The acceleration sensor 20has an X axis, a Y axis, and a Z axis. The X axis coincides with thelongitudinal direction of the shaft 24. The Z axis is orthogonal to theX axis and is parallel to the launch direction of the golf ball 2. The Yaxis is orthogonal to the X axis and the Z axis.

The sand wedge 18 is attached to a swing machine (Golf Laboratories,Inc.). The golf ball 2 or the standard ball is hit with the sand wedge18 under the condition of a head speed of 16 m/s. The hitting point inthis hitting is the sweet spot of the head 22. The acceleration in the Zaxis direction at the time of this hitting is measured by theacceleration sensor 20. The product of the total weight of the head 22,the shaft 24 and the acceleration sensor 20 and the acceleration is avertical force. The time from the time point at which the vertical forceis generated to the time point at which the vertical force is eliminatedis a contact time. The maximum value of the vertical force during thecontact time is a maximum vertical force. The average value of dataobtained by 12 hits is calculated.

In the second condition, the golf ball 2 or the standard ball is hitwith a putter 28 (trade name “Huntington Beach Soft Putter #4”,manufactured by Cleveland Golf Company, Inc.) shown in FIGS. 4 and 5 .FIGS. 4 and 5 also show the aforementioned acceleration sensor 20 (tradename “356A01”, manufactured by TOYO Corporation). The putter 28 has ahead 30 and a shaft 32. The head 30 includes a face 34 and a sole 35.The face 34 has a toe-side end point 36, a heel-side end point 38, and abottom edge line 40. In FIGS. 4 and 5 , reference character CPrepresents the central point of the face 34. The central point CP is ona center line CL. The distance from the center line CL to the heel-sideend point 38 is equal to the distance from the center line CL to thetoe-side end point 36. The distance from the bottom edge line 40 to thecentral point CP is 20 mm. On the bad side of the central point CP, theacceleration sensor 20 is fixed to the head 30.

The putter 28 is attached to a swing machine (Golf Laboratories, Inc.).The golf ball 2 or the standard ball is hit with the putter 28 under acondition that a rolling distance is 15 m on a green that is horizontaland whose speed measured by a stimpmeter is 10.0 m. The hitting point inthis hitting is the central point CP. The acceleration in the hittingdirection at the time of this hitting is measured by the accelerationsensor 20. The product of the total weight of the head 30 and theacceleration sensor 20 and the acceleration is a vertical force. Thetime from the time point at which the vertical force is generated to thetime point at which the vertical force is eliminated is a contact time.The maximum value of the vertical force during the contact time is amaximum vertical force. The average value of data obtained by 12 hits iscalculated.

The golf ball 2 according to the present embodiment satisfies thefollowing mathematical formulas (1) and (2).

(Fa/Fan)≤0.90  (1)

(Fa/Fan)²/(Fp/Fpn)≤0.90  (2)

Fa: the maximum vertical force of the golf ball 2 measured under thefirst condition.

Fan: the maximum vertical force of the standard hall measured under thefirst condition.

Fp: the maximum vertical force of the golf ball 2 measured under thesecond condition.

Fpn: the maximum vertical force of the standard ball measured under thesecond condition.

When the golf ball 2 in the rough is hit with a golf club, the grass issandwiched between the golf ball 2 and the head 22. The grass causes aslip of the golf ball 2. The slip decreases a spin rate, carrying thegolf ball 2 to a position that is not intended by the golf player. Upona shot with a short iron of the golf ball 2 that, satisfies the abovemathematical formula (1), even when the grass is sandwiched between thegolf ball 2 and the head 22, a slip is suppressed. The golf ball 2 hasexcellent spin performance upon a shot with a short iron. Furthermore,upon a shot with a short iron of the golf ball 2 that satisfies theabove mathematical formula (1), soft feel at impact is achieved. Withthe golf ball 2 that satisfies the above mathematical formula (2), bothsoft feel at impact upon a shot with a short iron and soft feel atimpact upon putting are achieved. With the golf ball 2, flightperformance upon a shot with a middle iron is not impaired.

In the golf ball 2 that satisfies the above mathematical formula (1),the ratio (Fa/Fan) is not greater than 0.90. From the viewpoint of spinperformance and feel at impact upon a shot with a short iron, the ratio(Fa/Fan) is more preferably not greater than 0.66 and particularlypreferably not greater than 0.84. The ratio (Fa/Fan) is preferably notless than 0.75.

In the golf ball 2 that satisfies the above mathematical formula (2),the ratio ((Fa/Fan)²/(Fp/Fpn)) is not greater than 0.90. From theviewpoint of feel at impact upon a shot with a short iron and uponputting, the ratio ((Fa/Fan)²/(Fp/Fpn)) is more preferably not greaterthan 0.80 and particularly preferably not greater than 0.77. The ratio((Fa/Fan)²/(Fp/Fpn)) is preferably not less than 0.70.

Examples of means for achieving the above mathematical formulas (1) and(2) include

(a) setting the hardness difference (H1s−H1o) of the core 4 to be large,(b) setting the hardness difference (H1s−H1₍₁₀₎) of the core 4 to belarge,(c) setting the ratio (H2/H3) of the hardness H2 of the mid layer 6 tothe hardness H3 of the cover 8 to be large,(d) setting the ratio of the sum (T2+T3) of the thickness T2 of the raidlayer 6 and the thickness T3 of the cover 8 to the diameter D1 of thecore 4 to be small, and the like.

Preferably, the golf ball 2 satisfies the following mathematical formula(3).

(Fp/Fpn)≤0.98  (3)

In other words, the ratio (Fp/Fpn) is not greater than 0.98. With thegolf ball 2, both soft feel at impact and firm feel are achieved uponputting. From this viewpoint, the ratio (Fp/Fpn) is more preferably notgreater than 0.96 and particularly preferably not greater than 0.95. Theratio (Fp/Fpn) is preferably not less than 0.80.

Preferably, the golf ball 2 satisfies the following mathematical formula(4).

(Tp/Tpn)≥1.01  (4)

Tp: the contact time of the golf ball 2 measured under the secondcondition.

Tpn: the contact time of the standard ball measured under the secondcondition.

In other words, the ratio (Tp/Tpn) is not less than 1.01. With the golfball 2, both soft feel at impact and firm feel are achieved uponputting. From this viewpoint, the ratio (Tp/Tpn) is more preferably notless than 1.02 and particularly preferably not less than 1.03. The ratio(Tp/Tpn) is preferably riot greater than 1.15.

Preferably, the golf ball 2 satisfies the following mathematical formula(5).

(Fp/Fpn)/(Tp/Tpn)≤0.98  (5)

In other words, the ratio ((Fp/Fpn)/(Tp/Tpn)) is not greater than 0.98.With the golf ball 2, both soft feel at impact and firm feel areachieved upon putting. From this viewpoint, the ratio((Fp/Fpn)/(Tp/Tpn)) is more preferably not greater than 0.95 andparticularly preferably not greater than 0.92. The ratio((Fp/Fpn)/(Tp/Tpn)) is preferably not less than 0.75.

EXAMPLES

The following will show the advantageous effects of golf balls accordingto Examples, but the scope disclosed in the present specification shouldnet be construed in a limited manner on the basis of the description ofthese Examples.

Example 1

A rubber composition was obtained by kneading 100 parts by weight of ahigh-cis polybutadiene (trade name “BR-60”, manufactured by JSRCorporation), 25.3 parts by weight of zinc diacrylate, 5.0 parts byweight of zinc oxide, 12.0 parts by weight of barium sulfate, 0.3 partsby weight of pentabromodiphenyl disulfide (PBDS), and 0.7 parts byweight of dicumyl peroxide (DCP). The rubber composition was placed intoa mold including upper and lower mold halves each having a hemisphericalcavity, and heated to obtain a core with a diameter of 39.7 mm.

A resin composition was obtained by kneading 50 parts by weight, of anionomer resin (the aforementioned “Himilan 1605”), 50 parts by weight ofanother ionomer resin (the aforementioned “Himilan AM7329”), 4 parts byweight of titanium dioxide, and 9 parts by weight of barium sulfate witha twin-screw kneading extruder. The core was placed into a moldincluding upper and lower mold halves each having a hemisphericalcavity. The core was covered with the resin composition by injectionmolding to form a mid layer. The thickness of the mid layer was 1.0 mm.

A paint composition (trade name “POLIN 750LE”, manufactured by SHINTOPAINT CO., LTD.) including a two-component curing type epoxy resin as abase polymer was prepared. The base material liquid of this paintcomposition includes 30 parts by weight of a bisphenol A type epoxyresin and 70 parts by weight of a solvent. The curing agent liquid ofthis paint composition includes 40 parts by weight of a modifiedpolyamide amine, 55 parts by weight of a solvent, and 5 parts by weightof titanium dioxide. The weight ratio of the base material liquid to thecuring agent liquid is 1/1. This paint composition was applied to thesurface of the mid layer with a spray gun, and kept at 23° C. for 12hours to obtain a reinforcing layer. The thickness of the reinforcinglayer was 10 μm.

A resin composition was obtained by kneading 100 parts by weight of athermoplastic polyurethane elastomer (the aforementioned “ElastollanNY84A”), 2 parts by weight of a lubricant (trade name “Wax Master VD”,manufactured by BASF Japan Ltd.), 4 parts by weight of titanium dioxide,and 0.2 parts by weight of a light stabilizer (trade name “JF-90”,manufactured by Johoku Chemical Co., Ltd.) with a twin-screw kneadingextruder. Half shells were obtained from this resin composition bycompression molding. The sphere including the core, the mid layer, andthe reinforcing layer was covered with two of these half shells. Thesehalf shells and the sphere were placed into a final mold including upperand lower mold halves each having a hemispherical cavity and having alarge number of pimples on its cavity face, and a cover was obtained bycompression molding. The thickness of the cover was 0.5 mm. Dimpleshaving a shape that is the inverted shape of the pimples were formed onthe cover.

A clear paint including a two-component curing type polyurethane as abase material was applied to the cover to form an inner paint layer.Another clear paint including a two-component curing type polyurethaneas a base material was applied to the inner paint layer to form an outerpaint layer. Thus, a golf ball of Example 1 with a diameter of about42.7 mm and a weight of about 45.3 g was obtained.

Example 2

A golf ball of Example 2 was obtained in the same manner as Example 1,except the specifications of the core, the mid layer, and the cover wereas shown in Tables 1 and 2 below.

Comparative Examples 1 and 2

As Comparative Example 1, a commercially available golf ball wasprepared. As Comparative Example 2, another commercially available golfball was prepared.

Flight Test, I#7

A 7-iron club (trade name “XXIO 11”, manufactured by Sumitomo RubberIndustries, Ltd., shaft product number: MP1100, shaft hardness: S, loftangle: 28.0°) was attached to a swing machine manufactured by GolfLaboratories, Inc. A golf ball was hit under the condition of a headspeed of 33 m/sec, and the spin rate and the flight distance weremeasured. The flight distance is the distance from the hitting spot tothe spot at which the golf ball stopped. The measurement was conducted12 times, and the average value of the obtained data was calculated.Furthermore, the evaluation was categorized as follows based on theaverage value of flight distance.

A: 148.0 yards or more

B: 145.0 yards or more and less than 148.0 yards

C: Less than 145.0 yards

The results are shown in Table 3 below.

Controllability

A sand wedge (trade name “RTX-3”, manufactured by Cleveland GolfCompany, Inc., loft angle: 58°) was attached to a swing machinemanufactured by Golf Laboratories, Inc. Two leaves of wild grass wereattached to the surface of a golf ball with adhesive tape. The golf ballwas set at a position where the wild grass was located between the golfball and the head of the sand wedge and the grooves of the head wereorthogonal to the longitudinal direction of the wild grass. The golfball was hit under the condition of a head speed of 16 m/s, and the spinrate was measured. The measurement was conducted 12 times, and theaverage value of the obtained data was calculated. Furthermore, theevaluation was categorized based on the average value.

A: 3500 rpm or more

B: 3000 rpm or more and less than 3500 rpm

C: Less than 3000 rpm

The results are shown in Table 3 below.

Feel at Impact, Wedge

A golf ball was hit with a driver by a tester, and a score was givenaccording to the following criteria.

0 points: Hard

2 points: Slightly hard

5 points: Normal

3 points: Slightly soft

10 points: Soft

The sum of scores by 50 testers was calculated, and the evaluation wascategorized as follows.

A: 340 points or more

B: 310 points or more and less than 340 points

C: Less than 310 points

The results are shown in Table 3 below.

Feel at Impact, Putter

A golf ball was hit with a putter by a tester, and a score was givenaccording to the following criteria.

0 points: Hard

2 points: Slightly hard

5 points: Normal

8 points: Slightly soft

10 points: Soft

The sum of scores by 50 testers was calculated, and the evaluation wascategorized as follows.

A: 330 points or more

B: 300 points or more and less than 330 points

C: Less than 300 points

The results are shown in Table 3 below.

TABLE 1 Composition (parts by weight) Ex. Ex. 1 2 Core BR 60 100 100Zinc diacrylate 25.3 25.8 Zinc oxide 5.0 5.0 Barium sulfate 12.0 13.4PBDS 0.3 0.3 DCP 0.7 0.7 Mid layer Himilan 1605 50 50 Himilan AM7329 5050 Titanium dioxide 4 4 Barium sulfate 9 — Cover Elastollan NY84A 100100 Wax Master VD 2 2 Titanium dioxide 4 4 JF-90 0.2 0.2

TABLE 2 Specifications Comp. Comp. Ex. Ex. Ex. Ex. Standard 1 2 1 2 ballCore D1 (mm) 39.7 39.7 39.3 39.1 39.0 H1o (Shore C) 56 61 66 62 62H1₍₁₀₎ (Shore C) 69 70 73 74 71 H1s (Shore C) 81 83 81 74 78 Mid layerT2 (mm) 1.0 1.0 0.7 1.0 1.4 H2 (Shore D) 66 65 66 68 71 H2s (Shore C) 9594 95 97 97 Cover T3 (mm) 0.5 0.5 1.0 0.8 0.5 H3 (Shore D) 31 31 45 4840 H3s (Shore C) 87 87 87 87 87 Outer paint layer Indentation 759 759 —— 971 depth (nm) CD (mm) 3.33 3.26 2.82 2.88 3.12 H1s − H1o 25 22 15 1211 (T2 + T3)/D1 0.038 0.038 0.043 0.046 0.049 H2/H3 2.13 2.10 1.47 1.421.78

TABLE 3 Evaluation Results Comp. Comp. Ex. Ex. Ex. Ex. Standard 1 2 1 2ball Fa/Fan 0.83 0.84 1.13 1.09 1.00 Fp/Fpn 0.90 0.95 1.02 1.06 1.00Tp/Tpn 1.06 1.03 0.96 0.93 1.00 (Fp/Fpn)/(Tp/Tpn) 0.85 0.92 1.06 1.141.00 (Fa/Fan)²/(Fp/Fpn) 0.77 0.75 1.25 1.12 1.00 Flight test I#7 Flightdistance 149.6 148.5 144.8 144.3 147.3 (yds.) Rank A A C C B Spin (rpm)4383 4516 4967 5028 4658 Controllability Spin (rpm) 4258 4111 2596 30933359 Rank A A C B B Feel at impact: wedge Score 348 393 307 310 325 RankA A C B B Feel at impact: putter Score 351 334 295 286 304 Rank A A C CB

As shown in Table 3, the golf ball of each Example has excellent flightperformance upon a shot with a middle iron, excellent spin performanceupon a shot with a short iron, excellent feel at impact upon a shot witha short iron, and excellent feel at impact upon putting. From theevaluation results, advantages of the golf ball are clear.

Disclosure Items

Each of the following items is the disclosure of a preferred embodiment.

Item 1

A golf ball including a core, a mid layer positioned outside the core,and a cover positioned outside the mid layer, the golf ball satisfyingthe following mathematical formulas (1) and (2),

(Fa/Fan)≤0.90  (1),

(Fa/Fan)²/(Fp/Fpn)≤0.90  (2),

wherein Fa represents a maximum vertical force of the golf ball measuredunder a first condition. Fan represents a maximum vertical force of astandard ball measured under the first condition, Fp represents amaximum vertical force of the golf ball measured under a secondcondition, and Fpn represents a maximum vertical force of the standardball measured under the second condition.

Item 2

The golf ball according to Item 1, wherein the golf ball satisfies themathematical formula (3),

(Fp/Fpn)≤0.98  (3).

Item 3

The golf ball according to Item 1 or 2, wherein the golf ball satisfiesthe mathematical formula (4),

(Tp/Tpn)≥1.01  (4),

wherein Tp represents a contact time of the golf ball measured under thesecond condition, and Tpn represents a contact time of the standard ballmeasured under the second condition.

Item 4

The golf ball according to Item 3, wherein the golf ball satisfies themathematical formula (5),

(Fp/Fpn)/(Tp/Tpn)≤0.98  (5).

Item 5

The golf ball according to any one of Items 1 to 4, wherein an amount ofcompressive deformation CD of the golf ball measured under a conditionthat an initial load is 98 N and a final load is 1275 N is not less than3.00 mm.

Item 6

The golf ball according to any one of Items 1 to 5, wherein a surfacehardness H2s (Shore C) of the mid layer is greater than a surfacehardness H1s (Shore C) of the core and is greater than a surfacehardness H3s (Shore C) of the cover.

Item 7

The golf ball according to any one of Items 1 to 6, wherein a difference(H1s−H1o) between a surface hardness H1s (Shore C) and a centralhardness H1o (Shore C) of the core is not less than 14.

Item 8

The golf ball according to any one of Items 1 to 7, wherein a ratio of asum bold (T2+T3) of a thickness T2 of the mid layer and a thickness T3of the cover to a diameter D1 of the core is not greater than 0.042.

Item 9

The golf ball according to any one of Items 1 to 8, wherein a ratio(H2/H3) of a hardness H2 (Shore D) of the mid layer to a hardness H3(Shore D) of the cover is not less than 1.80.

Item 10

The golf ball according to any one of Items 1 to 9, further includingone or more paint layers positioned outside the cover, wherein

an indentation depth of an outermost paint layer when a load is 30 mgfis not less than 300 nm and not greater than 3000 nm.

The aforementioned golf ball is suitable for, for example, playing golfon golf courses and practicing at driving ranges. The above descriptionsare merely illustrative examples, and various modifications can be madewithout departing from the principles of the present invention.

What is claimed is:
 1. A golf ball comprising a core, a mid layerpositioned outside the core, and a cover positioned outside the midlayer, the golf ball satisfying the following mathematical formulas (1)and (2),(Fa/Fan)≤0.90  (1),(Fa/Fan)²/(Fp/Fpn)≤0.90  (2), wherein Fa represents a maximum verticalforce of the golf ball measured under a first condition, Fan representsa maximum vertical force of a standard ball measured under the firstcondition, Fp represents a maximum vertical force of the golf ballmeasured under a second condition, and Fpn represents a maximum verticalforce of the standard ball measured under the second condition.
 2. Thegolf ball according to claim 1, wherein the golf ball satisfies themathematical formula (3),(Fp/Fpn)≤0.98  (3).
 3. The golf ball according to claim 1, wherein thegolf ball satisfies the mathematical formula (4),(Tp/Tpn)≥1.01  (4), wherein Tp represents a contact time of the golfball measured under the second condition, and Tpn represents a contacttime of the standard ball measured under the second condition.
 4. Thegolf ball according to claim 3, wherein the golf ball satisfies themathematical formula (5),(Fp/Fpn)/(Tp/Tpn)≤0.93  (5).
 5. The golf ball according to claim 1,wherein an amount of compressive deformation CD of the golf ballmeasured under a condition that an initial load is 98 N and a final loadis 1275 N is not less than 3.00 nm.
 6. The golf ball according to claim1, wherein a surface hardness H2s (Shore C) of the mid layer is greaterthan a surface hardness H1s (Shore C) of the core and is greater than asurface hardness H3s (Shore C) of the cover.
 7. The golf ball accordingto claim 1, wherein a difference (H1s−H1o) between a surface hardnessH1s (Shore C) and a central hardness H1o (Shore C) of the core is notless than
 14. 8. The golf ball according to claim 1, wherein a ratio ofa sum (T2+T3) of a thickness T2 of the mid layer and a thickness T3 ofthe cover to a diameter D1 of the core is not greater than 0.042.
 9. Thegolf ball according to claim 1, wherein a ratio (H2/H3) of a hardness H2(Shore D) of the mid layer to a hardness H3 (Shore D) of the cover isnot less than 1.80.
 10. The golf ball according to claim 1, furthercomprising one or more paint layers positioned outside the cover,wherein an indentation depth of an outermost paint layer when a load is30 mgf is not less than 300 nm and not greater than 3000 nm.